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Abstract Given a set of alternatives, X and a set of value, or utility, functions, V , on X , contemporary work in the Decision Theory field deals with the reduction of X to some acceptable subset Y . This paper deals with the various ways in which this may be done, more specifically with the optimal set, M ( X , V ), the efficient set E ( X , V ) and efficient sets ϵ ( X , f ), ϵ ( X , f ), ϵ ( X , f ), when the value of an alternative can be expressed in terms of a multi-objective vector f on X . Relationships between these various sets are explained. The importance of the differences and similarities is seen to depend on the nature of the circumstances faced by the decision analyst at each stage of the evolutionary process of analysis, and upon their use for computational purposes. Some contemporary work (e.g. portfolio analysis) is examined within this framework.
Beaumont et al. (Sun,) studied this question.